Construction géométrique

Sommes de vecteurs



Construire les points $D$ et $E$ tels que: $\displaystyle \bullet\ \ \overrightarrow{AD}=\overrightarrow{AB}+\overrightarro...
...et\ \ \overrightarrow{AE}=2\overrightarrow{BC}+\dfrac{1}{2}\overrightarrow{AC}$

\begin{pspicture}(0.5,0)(5,4)
\rput(2,3){\large$\times $}\rput(1.7,3.2){$A$}
\...
...ut(0.7,0.8){$B$}
\rput(4,1){\large$\times $}\rput(4.3,1.2){$C$}
\end{pspicture}



Construire les points $F$ et $G$ tels que: $\displaystyle \bullet\ \ \overrightarrow{CF}=-\overrightarrow{AD}+\overrightarr...
...rightarrow{DG}=\dfrac{1}{2}\overrightarrow{BA}-\dfrac{3}{2}\overrightarrow{BD}$

\begin{pspicture}(0,0)(5,5)\rput(3,4){\large$\times $}\rput(2.7,4.2){$A$}
\rp...
...3,2.5){$D$}
\rput(2,-1){\large$\times $}\rput(1.6,-0.9){$C$}
%
\end{pspicture}


Solution:


Construire les points $D$ et $E$ tels que $\displaystyle \bullet\ \ \overrightarrow{AD}=\overrightarrow{AB}+\overrightarro...
...et\ \ \overrightarrow{AE}=2\overrightarrow{BC}+\dfrac{1}{2}\overrightarrow{AC}$

\begin{pspicture}(0.5,0)(5,4)
\rput(2,3){\large$\times $}\rput(1.7,3.2){$A$}
\...
...t(9.2,2.8){$\dfrac{1}{2}\overrightarrow{AC}$}
\rput(9,1.7){$E$}
\end{pspicture}



Construire les points $F$ et $G$ tels que:
$\displaystyle \bullet\ \ \overrightarrow{CF}=-\overrightarrow{AD}+\overrightarr...
...rightarrow{DG}=\dfrac{1}{2}\overrightarrow{BA}-\dfrac{3}{2}\overrightarrow{BD}$
\begin{pspicture}(0,0)(5,5)
\rput(3,4){\large$\times $}\rput(2.7,4.2){$A$}
\rp...
...(2,3.5){-$\dfrac{3}{2}\overrightarrow{BD}$}
\rput(0.5,3.1){$G$}
\end{pspicture}




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